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Journal Articles Journal of Differential Equations Year : 2015

Mathematical analysis of a sharp-diffuse interfaces model for seawater intrusion

Abstract

We consider a new model mixing sharp and diffuse interface approaches for seawater intrusion phe- nomena in free aquifers. More precisely, a phase field model is introduced in the boundary conditions on the virtual sharp interfaces. We thus include in the model the existence of diffuse transition zones but we preserve the simplified structure allowing front tracking. The three-dimensional problem then reduces to a two-dimensional model involving a strongly coupled system of partial differential equations of parabolic type describing the evolution of the depths of the two free surfaces, that is the interface between salt- and freshwater and the water table. We prove the existence of a weak solution for the model completed with ini- tial and boundary conditions. We also prove that the depths of the two interfaces satisfy a coupled maximum principle.

Dates and versions

hal-01273793 , version 1 (13-02-2016)

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Catherine Choquet, Moussa Mory Diédhiou, Carole Rosier. Mathematical analysis of a sharp-diffuse interfaces model for seawater intrusion. Journal of Differential Equations, 2015, ⟨10.1016/j.jde.2015.05.005⟩. ⟨hal-01273793⟩
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